29.21.17 problem 593

Internal problem ID [5187]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 593
Date solved : Sunday, March 30, 2025 at 06:48:49 AM
CAS classification : [[_Abel, `2nd type`, `class C`]]

\begin{align*} \left (\operatorname {g0} \left (x \right )+y \operatorname {g1} \left (x \right )\right ) y^{\prime }&=\operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3} \end{align*}

✗ Maple

ode:=(g0(x)+y(x)*g1(x))*diff(y(x),x) = f0(x)+f1(x)*y(x)+f2(x)*y(x)^2+f3(x)*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(g0[x]+y[x] g1[x])D[y[x],x]==f0[x]+f1[x] y[x]+f2[x] y[x]^2+f3[x] y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
g0 = Function("g0") 
g1 = Function("g1") 
f0 = Function("f0") 
f1 = Function("f1") 
f2 = Function("f2") 
f3 = Function("f3") 
ode = Eq((g0(x) + g1(x)*y(x))*Derivative(y(x), x) - f0(x) - f1(x)*y(x) - f2(x)*y(x)**2 - f3(x)*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out